As shown in FIG. 1, a bullet or other projectile traverses a curved trajectory as it falls and decelerates while traveling from a point at which it departs a weapon to a point of impact (i.e., a target location). Due to its curved trajectory, the projectile will intersect an aiming line of sight at one or two ranges and pass below or above it at other ranges. A sight-in range (so-called zero range, zeroed-in range, or true zero) of the weapon and sight combination is the range at which a line of sight intersects a projectile's curved trajectory at a known horizontal reference distance, such as 200 yards or meters, so that projectiles shot from the weapon impact a target at the reference distance coinciding with a reference aiming point of crosshairs or another aiming mark of a riflescope (or other sighting device).
The aforementioned trajectory and the projectile's position thereon depend on ballistic characteristics, such as projectile weight, drag, and initial velocity (e.g., muzzle velocity), and on other factors characterized by exterior point mass ballistics. The principles of exterior point mass ballistics, or simply exterior ballistics, are well understood and have been expressed in mathematical terms in scientific literature. See, for example, E. J. McShane et al., “Exterior Ballistics,” University of Denver Press (1953); Bryan Litz, “Applied Ballistics for Long Range Shooting,” Applied Ballistics, LLC, 2nd edition (2011); and R. L. McCoy, “Modern Exterior Ballistics,” Schiffer Publishing, Ltd., 2nd edition (2012), all of which are incorporated herein by reference as background information. In short, however, exterior ballistics equations may be used for calculating a projectile's position along its curved trajectory.
The aforementioned equations have been implemented, to various degrees, in exterior ballistics software applications. Ballistics software typically includes a library of ballistic coefficients and muzzle velocities for a variety of particular cartridges (also called an ammunition load, or simply, load). A user selects from the library an ammunition type, which serves as an input for ballistic calculations performed by the software. The ballistics software also allows a user to input target conditions, such as the elevation angle from level shooting and the range to the target; environmental conditions, including geospatial and meteorological conditions; and weapon configuration conditions such as sight height and zero range. Based on the user input, ballistics software applications may then calculate and provide as output various ballistics trajectory parameters. A calculated ballistics trajectory parameter may define a calculated trajectory in terms of projectile drop amounts that are the vertical component from a line of departure (e.g., a bore centerline) to points along the calculated trajectory, projectile path amounts at trajectory points perpendicular to a line of sight, or other ballistics trajectory parameters used to make an aiming adjustment in order to hit a target at a given range.
Aiming adjustments are designated in terms of inches or centimeters at the target range. Another way to designate vertical aiming adjustment is in terms of minutes of angle (MOA). For example, most riflescopes include adjustment knob mechanisms that facilitate mechanical elevation adjustments in ¼ MOA or ½ MOA increments. Accordingly, ballistic software may output as ballistic solutions aiming adjustment amounts (i.e., projectile drop or path) in terms of MOA or distance (height in inches). The ballistic solution may include vertical aiming adjustments and horizontal aiming adjustments.
The vertical aiming adjustments, also called elevation adjustments, are typically established by holdover and holdunder adjustments (also referred to as come-up and come-down adjustments) or mechanical elevation adjustment to a riflescope or other aiming device (relative to the weapon on which the aiming device is mounted). Similarly, horizontal aiming adjustments are made by aiming to the left or right, or by mechanical adjustments, and are commonly referred to as windage adjustments.
Some ballistic software programs have been adapted to operate on a handheld computer. For example, U.S. Pat. No. 6,516,699 of Sammut et al. describes a personal digital assistant (PDA) running an exterior ballistics software program. Other ballistic software programs are deployed in laser rangefinder binoculars and projectile-weapon aiming systems rigidly affixed to a weapon and commonly embodied as a riflescope. Riflescopes include reticles for aiming at locations indicated by a reticle aiming mark. A reticle aiming mark defines an aiming point at which a straight aiming line of sight intersects at a discrete distance a bullet's or other projectile's curved trajectory.